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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2020-11-10 mar. 12:55 --> <!-- 2020-11-10 mar. 13:00 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Piezoelectric Force Sensor - Test Bench</title> <title>Piezoelectric Force Sensor - Test Bench</title>
<meta name="generator" content="Org mode" /> <meta name="generator" content="Org mode" />
@ -34,17 +34,17 @@
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orga1465ad">1. Change of Stiffness due to Sensors stack being open/closed circuit</a> <li><a href="#orgfa4ffe0">1. Change of Stiffness due to Sensors stack being open/closed circuit</a>
<ul> <ul>
<li><a href="#orgd924c73">1.1. Load Data</a></li> <li><a href="#org664356d">1.1. Load Data</a></li>
<li><a href="#org59cc20a">1.2. Transfer Functions</a></li> <li><a href="#orgb329298">1.2. Transfer Functions</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org76a1832">2. Generated Number of Charge / Voltage</a> <li><a href="#orgcc12929">2. Generated Number of Charge / Voltage</a>
<ul> <ul>
<li><a href="#org1fa991d">2.1. Steps</a></li> <li><a href="#org7a46587">2.1. Steps</a></li>
<li><a href="#org5e9eb44">2.2. Add Parallel Resistor</a></li> <li><a href="#org9938615">2.2. Add Parallel Resistor</a></li>
<li><a href="#org15676e1">2.3. Sinus</a></li> <li><a href="#org3e71d2e">2.3. Sinus</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -56,20 +56,20 @@ In this document is studied how a piezoelectric stack can be used to measured th
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>Section <a href="#org887b61a">1</a>: the effect of the input impedance of the electronics connected to the force sensor stack on the stiffness of the stack is studied</li> <li>Section <a href="#org574ce5b">1</a>: the effect of the input impedance of the electronics connected to the force sensor stack on the stiffness of the stack is studied</li>
<li>Section <a href="#org2b5f630">2</a>:</li> <li>Section <a href="#org3d96d6c">2</a>:</li>
</ul> </ul>
<div id="outline-container-orga1465ad" class="outline-2"> <div id="outline-container-orgfa4ffe0" class="outline-2">
<h2 id="orga1465ad"><span class="section-number-2">1</span> Change of Stiffness due to Sensors stack being open/closed circuit</h2> <h2 id="orgfa4ffe0"><span class="section-number-2">1</span> Change of Stiffness due to Sensors stack being open/closed circuit</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
<a id="org887b61a"></a> <a id="org574ce5b"></a>
</p> </p>
</div> </div>
<div id="outline-container-orgd924c73" class="outline-3"> <div id="outline-container-org664356d" class="outline-3">
<h3 id="orgd924c73"><span class="section-number-3">1.1</span> Load Data</h3> <h3 id="org664356d"><span class="section-number-3">1.1</span> Load Data</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">oc = load(<span class="org-string">'identification_open_circuit.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'encoder'</span>, <span class="org-string">'u'</span>); <pre class="src src-matlab">oc = load(<span class="org-string">'identification_open_circuit.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'encoder'</span>, <span class="org-string">'u'</span>);
@ -79,8 +79,8 @@ sc = load(<span class="org-string">'identification_short_circuit.mat'</span>, <s
</div> </div>
</div> </div>
<div id="outline-container-org59cc20a" class="outline-3"> <div id="outline-container-orgb329298" class="outline-3">
<h3 id="org59cc20a"><span class="section-number-3">1.2</span> Transfer Functions</h3> <h3 id="orgb329298"><span class="section-number-3">1.2</span> Transfer Functions</h3>
<div class="outline-text-3" id="text-1-2"> <div class="outline-text-3" id="text-1-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">Ts = 1e<span class="org-type">-</span>4; <span class="org-comment">% Sampling Time [s]</span> <pre class="src src-matlab">Ts = 1e<span class="org-type">-</span>4; <span class="org-comment">% Sampling Time [s]</span>
@ -98,26 +98,26 @@ win = hann(ceil(10<span class="org-type">/</span>Ts));
</div> </div>
<div id="org3c75143" class="figure"> <div id="org07156da" class="figure">
<p><img src="figs/stiffness_force_sensor_coherence.png" alt="stiffness_force_sensor_coherence.png" /> <p><img src="figs/stiffness_force_sensor_coherence.png" alt="stiffness_force_sensor_coherence.png" />
</p> </p>
</div> </div>
<div id="org4424b1c" class="figure"> <div id="org4e249d7" class="figure">
<p><img src="figs/stiffness_force_sensor_bode.png" alt="stiffness_force_sensor_bode.png" /> <p><img src="figs/stiffness_force_sensor_bode.png" alt="stiffness_force_sensor_bode.png" />
</p> </p>
</div> </div>
<div id="org216fcc3" class="figure"> <div id="org503058b" class="figure">
<p><img src="figs/stiffness_force_sensor_bode_zoom.png" alt="stiffness_force_sensor_bode_zoom.png" /> <p><img src="figs/stiffness_force_sensor_bode_zoom.png" alt="stiffness_force_sensor_bode_zoom.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Zoom on the change of resonance</p> <p><span class="figure-number">Figure 3: </span>Zoom on the change of resonance</p>
</div> </div>
<div class="important" id="org9ea3712"> <div class="important" id="org93bdd08">
<p> <p>
The change of resonance frequency / stiffness is very small and is not important here. The change of resonance frequency / stiffness is very small and is not important here.
</p> </p>
@ -127,11 +127,11 @@ The change of resonance frequency / stiffness is very small and is not important
</div> </div>
</div> </div>
<div id="outline-container-org76a1832" class="outline-2"> <div id="outline-container-orgcc12929" class="outline-2">
<h2 id="org76a1832"><span class="section-number-2">2</span> Generated Number of Charge / Voltage</h2> <h2 id="orgcc12929"><span class="section-number-2">2</span> Generated Number of Charge / Voltage</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a id="org2b5f630"></a> <a id="org3d96d6c"></a>
</p> </p>
<p> <p>
Two stacks are used as actuator (in parallel) and one stack is used as sensor. Two stacks are used as actuator (in parallel) and one stack is used as sensor.
@ -142,8 +142,8 @@ The amplifier gain is 20V/V (Cedrat LA75B).
</p> </p>
</div> </div>
<div id="outline-container-org1fa991d" class="outline-3"> <div id="outline-container-org7a46587" class="outline-3">
<h3 id="org1fa991d"><span class="section-number-3">2.1</span> Steps</h3> <h3 id="org7a46587"><span class="section-number-3">2.1</span> Steps</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'force_sensor_steps.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'encoder'</span>, <span class="org-string">'u'</span>, <span class="org-string">'v'</span>); <pre class="src src-matlab">load(<span class="org-string">'force_sensor_steps.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'encoder'</span>, <span class="org-string">'u'</span>, <span class="org-string">'v'</span>);
@ -163,7 +163,7 @@ xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-stri
</div> </div>
<div id="orgf889803" class="figure"> <div id="orgda3ef57" class="figure">
<p><img src="figs/force_sen_steps_time_domain.png" alt="force_sen_steps_time_domain.png" /> <p><img src="figs/force_sen_steps_time_domain.png" alt="force_sen_steps_time_domain.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Time domain signal during the 3 actuator voltage steps</p> <p><span class="figure-number">Figure 4: </span>Time domain signal during the 3 actuator voltage steps</p>
@ -262,7 +262,7 @@ Rin = abs(mean(tau))<span class="org-type">/</span>Cp;
The input impedance of the Speedgoat&rsquo;s ADC should then be close to \(1.5\,M\Omega\) (specified at \(1\,M\Omega\)). The input impedance of the Speedgoat&rsquo;s ADC should then be close to \(1.5\,M\Omega\) (specified at \(1\,M\Omega\)).
</p> </p>
<div class="important" id="org572654b"> <div class="important" id="org7c6e263">
<p> <p>
How can we explain the voltage offset? How can we explain the voltage offset?
</p> </p>
@ -270,12 +270,12 @@ How can we explain the voltage offset?
</div> </div>
<p> <p>
As shown in Figure <a href="#org7c2c57f">5</a> (taken from (<a href="#citeproc_bib_item_1">Reza and Andrew 2006</a>)), an input voltage offset is due to the input bias current \(i_n\). As shown in Figure <a href="#org1036a3b">5</a> (taken from (<a href="#citeproc_bib_item_1">Reza and Andrew 2006</a>)), an input voltage offset is due to the input bias current \(i_n\).
</p> </p>
<div id="org7c2c57f" class="figure"> <div id="org1036a3b" class="figure">
<p><img src="figs/force_sensor_model_electronics.png" alt="force_sensor_model_electronics.png" /> <p><img src="figs/force_sensor_model_electronics_without_R.png" alt="force_sensor_model_electronics_without_R.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Model of a piezoelectric transducer (left) and instrumentation amplifier (right)</p> <p><span class="figure-number">Figure 5: </span>Model of a piezoelectric transducer (left) and instrumentation amplifier (right)</p>
</div> </div>
@ -338,18 +338,18 @@ Which is much more acceptable.
</div> </div>
</div> </div>
<div id="outline-container-org5e9eb44" class="outline-3"> <div id="outline-container-org9938615" class="outline-3">
<h3 id="org5e9eb44"><span class="section-number-3">2.2</span> Add Parallel Resistor</h3> <h3 id="org9938615"><span class="section-number-3">2.2</span> Add Parallel Resistor</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<p> <p>
A resistor \(R_p \approx 100\,k\Omega\) is added in parallel with the force sensor as shown in Figure <a href="#org1fac5a7">6</a>. A resistor \(R_p \approx 100\,k\Omega\) is added in parallel with the force sensor as shown in Figure <a href="#orgbf8a90f">6</a>.
</p> </p>
<div id="org1fac5a7" class="figure"> <div id="orgbf8a90f" class="figure">
<p><img src="figs/force_sensor_model_electronics_without_R.png" alt="force_sensor_model_electronics_without_R.png" /> <p><img src="figs/force_sensor_model_electronics.png" alt="force_sensor_model_electronics.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Model of a piezoelectric transducer (left) and instrumentation amplifier (right) with added resistor \(R_p\)</p> <p><span class="figure-number">Figure 6: </span>Model of a piezoelectric transducer (left) and instrumentation amplifier (right) with the additional resistor \(R_p\)</p>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
@ -370,7 +370,7 @@ xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-stri
</div> </div>
<div id="org29964b5" class="figure"> <div id="orgf9378d8" class="figure">
<p><img src="figs/force_sen_steps_time_domain_par_R.png" alt="force_sen_steps_time_domain_par_R.png" /> <p><img src="figs/force_sen_steps_time_domain_par_R.png" alt="force_sen_steps_time_domain_par_R.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Time domain signal during the actuator voltage steps</p> <p><span class="figure-number">Figure 7: </span>Time domain signal during the actuator voltage steps</p>
@ -514,8 +514,8 @@ This validates the model of the ADC and the effectiveness of the added resistor.
</div> </div>
</div> </div>
<div id="outline-container-org15676e1" class="outline-3"> <div id="outline-container-org3e71d2e" class="outline-3">
<h3 id="org15676e1"><span class="section-number-3">2.3</span> Sinus</h3> <h3 id="org3e71d2e"><span class="section-number-3">2.3</span> Sinus</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'force_sensor_sin.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'encoder'</span>, <span class="org-string">'u'</span>, <span class="org-string">'v'</span>); <pre class="src src-matlab">load(<span class="org-string">'force_sensor_sin.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'encoder'</span>, <span class="org-string">'u'</span>, <span class="org-string">'v'</span>);
@ -528,11 +528,11 @@ t = t(t<span class="org-type">&gt;</span>25);
</div> </div>
<p> <p>
The driving voltage is a sinus at 0.5Hz centered on 3V and with an amplitude of 3V (Figure <a href="#org1fbf89d">8</a>). The driving voltage is a sinus at 0.5Hz centered on 3V and with an amplitude of 3V (Figure <a href="#org2ae5f53">8</a>).
</p> </p>
<div id="org1fbf89d" class="figure"> <div id="org2ae5f53" class="figure">
<p><img src="figs/force_sensor_sin_u.png" alt="force_sensor_sin_u.png" /> <p><img src="figs/force_sensor_sin_u.png" alt="force_sensor_sin_u.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Driving Voltage</p> <p><span class="figure-number">Figure 8: </span>Driving Voltage</p>
@ -552,11 +552,11 @@ The full stroke as measured by the encoder is:
<p> <p>
Its signal is shown in Figure <a href="#org1d74efa">9</a>. Its signal is shown in Figure <a href="#org3458f57">9</a>.
</p> </p>
<div id="org1d74efa" class="figure"> <div id="org3458f57" class="figure">
<p><img src="figs/force_sensor_sin_encoder.png" alt="force_sensor_sin_encoder.png" /> <p><img src="figs/force_sensor_sin_encoder.png" alt="force_sensor_sin_encoder.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Encoder measurement</p> <p><span class="figure-number">Figure 9: </span>Encoder measurement</p>
@ -567,7 +567,7 @@ The generated voltage by the stack is shown in Figure
</p> </p>
<div id="org077a6d7" class="figure"> <div id="orga69980e" class="figure">
<p><img src="figs/force_sensor_sin_stack.png" alt="force_sensor_sin_stack.png" /> <p><img src="figs/force_sensor_sin_stack.png" alt="force_sensor_sin_stack.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </span>Voltage measured on the stack used as a sensor</p> <p><span class="figure-number">Figure 10: </span>Voltage measured on the stack used as a sensor</p>
@ -582,10 +582,10 @@ The capacitance of the stack is
</div> </div>
<p> <p>
The corresponding generated charge is then shown in Figure <a href="#org4baf062">11</a>. The corresponding generated charge is then shown in Figure <a href="#orgeafdaf5">11</a>.
</p> </p>
<div id="org4baf062" class="figure"> <div id="orgeafdaf5" class="figure">
<p><img src="figs/force_sensor_sin_charge.png" alt="force_sensor_sin_charge.png" /> <p><img src="figs/force_sensor_sin_charge.png" alt="force_sensor_sin_charge.png" />
</p> </p>
<p><span class="figure-number">Figure 11: </span>Generated Charge</p> <p><span class="figure-number">Figure 11: </span>Generated Charge</p>
@ -593,7 +593,7 @@ The corresponding generated charge is then shown in Figure <a href="#org4baf062"
<p> <p>
The relation between the generated voltage and the measured displacement is almost linear as shown in Figure <a href="#org8b9df34">12</a>. The relation between the generated voltage and the measured displacement is almost linear as shown in Figure <a href="#org83e4a49">12</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -602,7 +602,7 @@ The relation between the generated voltage and the measured displacement is almo
</div> </div>
<div id="org8b9df34" class="figure"> <div id="org83e4a49" class="figure">
<p><img src="figs/force_sensor_linear_relation.png" alt="force_sensor_linear_relation.png" /> <p><img src="figs/force_sensor_linear_relation.png" alt="force_sensor_linear_relation.png" />
</p> </p>
<p><span class="figure-number">Figure 12: </span>Almost linear relation between the relative displacement and the generated voltage</p> <p><span class="figure-number">Figure 12: </span>Almost linear relation between the relative displacement and the generated voltage</p>
@ -631,7 +631,7 @@ With a 16bits ADC, the resolution will then be equals to (in [nm]):
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-11-10 mar. 12:55</p> <p class="date">Created: 2020-11-10 mar. 13:00</p>
</div> </div>
</body> </body>
</html> </html>

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@ -165,8 +165,6 @@ In this document is studied how a piezoelectric stack can be used to measured th
<<sec:charge_voltage_estimation>> <<sec:charge_voltage_estimation>>
** Introduction :ignore: ** Introduction :ignore:
Two stacks are used as actuator (in parallel) and one stack is used as sensor. Two stacks are used as actuator (in parallel) and one stack is used as sensor.
The amplifier gain is 20V/V (Cedrat LA75B). The amplifier gain is 20V/V (Cedrat LA75B).
@ -276,11 +274,11 @@ The input impedance of the Speedgoat's ADC should then be close to $1.5\,M\Omega
How can we explain the voltage offset? How can we explain the voltage offset?
#+end_important #+end_important
As shown in Figure [[fig:force_sensor_model_electronics]] (taken from cite:reza06_piezoel_trans_vibrat_contr_dampin), an input voltage offset is due to the input bias current $i_n$. As shown in Figure [[fig:force_sensor_model_electronics_without_R]] (taken from cite:reza06_piezoel_trans_vibrat_contr_dampin), an input voltage offset is due to the input bias current $i_n$.
#+name: fig:force_sensor_model_electronics #+name: fig:force_sensor_model_electronics_without_R
#+caption: Model of a piezoelectric transducer (left) and instrumentation amplifier (right) #+caption: Model of a piezoelectric transducer (left) and instrumentation amplifier (right)
[[file:figs/force_sensor_model_electronics.png]] [[file:figs/force_sensor_model_electronics_without_R.png]]
The estimated input bias current is then: The estimated input bias current is then:
#+begin_src matlab #+begin_src matlab
@ -330,11 +328,11 @@ With this parallel resistance value, the voltage offset would be:
Which is much more acceptable. Which is much more acceptable.
** Add Parallel Resistor ** Add Parallel Resistor
A resistor $R_p \approx 100\,k\Omega$ is added in parallel with the force sensor as shown in Figure [[fig:force_sensor_model_electronics_without_R]]. A resistor $R_p \approx 100\,k\Omega$ is added in parallel with the force sensor as shown in Figure [[fig:force_sensor_model_electronics]].
#+name: fig:force_sensor_model_electronics_without_R #+name: fig:force_sensor_model_electronics
#+caption: Model of a piezoelectric transducer (left) and instrumentation amplifier (right) with added resistor $R_p$ #+caption: Model of a piezoelectric transducer (left) and instrumentation amplifier (right) with the additional resistor $R_p$
[[file:figs/force_sensor_model_electronics_without_R.png]] [[file:figs/force_sensor_model_electronics.png]]
#+begin_src matlab #+begin_src matlab
load('force_sensor_steps_R_82k7.mat', 't', 'encoder', 'u', 'v'); load('force_sensor_steps_R_82k7.mat', 't', 'encoder', 'u', 'v');